A huge majority of "very high-ranking Shi'ites" disagreed with the government and contested its religious values, he said.
Iranian authorities have been unable to stop a protest movement, set off by the disputed June re-election of President Mahmoud Ahmadinejad, despite intensifying their crackdown after eight people were killed during protests on Dec. 27.
"We can all see that the regime is under threat from people who are very determined, Iranians, some of them very religious, from the Shi'ite hierarchy," Kouchner said on RTL radio.
"Yes, the regime is under threat from internal opposition and I don't know what it could lead to," he said.
Iranian opposition leader Mirhossein Mousavi said on Friday his country was in serious crisis and called for reforms, saying he was ready to die for the protest movement.
Asked whether he hoped the Iranian government would be overthrown, Kouchner said, "It's not for me to wish for that or not. For our part, we continue to talk to the Iranians."
France is one of several Western countries at loggerheads with Ahmadinejad's government over Iran's nuclear programme.
Kouchner expressed frustration with what he described as Iran's latest "diplomatic pirouette" and said it was "unfortunately not possible" to talk seriously with Tehran about its nuclear development.
Iran rebuffed a Western deadline of Dec. 31, 2009, to accept an enrichment fuel deal aimed at calming international fears it is trying to build nuclear weapons. Iran denies this.
Kouchner noted that the deadline had now expired but did not say what he would do next.
The United States and its allies are weighing focused sanctions against the Iranian leadership rather than broad-based penalties that they fear would harm the protest movement, officials and diplomats say.
(Reporting by Estelle Shirbon; Editing by Louise Ireland)
